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DOE OSTI2025

Linearized Pair-Density Functional Theory with Spin–Orbit Coupling

Here, we include spin–orbit coupling (SOC) effects in linearized pair-density functional theory (L-PDFT), which is a multistate extension of multiconfiguration pair-density functional theory (MC-PDFT). Both 1-electron and 2-electron SOC integrals are computed using Breit-Pauli and Douglas–Kroll–Hess Hamiltonians in the atomic mean-field approximation. SO-L-PDFT removes the unphysical J-symmetry breaking observed in MC-PDFT. The accuracy of SO-L-PDFT is validated by calculations of zero-field splittings, fine-structure excitation energies, and low-energy excited-state spectra for a diverse group of atoms and molecules spanning the whole range of the periodic table, including atoms of groups 3, 11, and 13–17, the Ce 3+ and U 5+ ions, group 16 monohydrides, group 17 monoxides, lanthanide hexachlorides ([CeCl 6 ] 3− , [PrCl 6 ] 3− , and [NdCl 6 ] 3− ), actinyl ions ([UO 2 ] + , [NpO 2 ] 2+ ), and tricarbonatoactinyl complexes ([UO 2 (CO 3 ) 3 ] 5− , [NpO 2 (CO 3 ) 3 ] 4− ). We also compare the results to new spin–orbit-inclusive calculations by single-state and multistate multireference perturbation theory.

Hamiltonians↗

DOE OSTI2023

Multiconfiguration Pair-Density Functional Theory for Vertical Excitation Energies in Actinide Molecules

Modeling actinides with electronic structure theories is challenging because these systems present a strong ligand field and metal–ligand covalency. Here, we systematically investigate the effectiveness of pair-density functional theory (PDFT) for the calculation of vertical excitation energies in An(III), [An III Cl 6 ] 3– , and [An VI O 2 ] 2+ (An = U, Np, Pu, and Am). We compare the performance of PDFT, hybrid PDFT, and multistate PDFT with traditional active-space methods followed by perturbation theory, like multistate CASPT2, and with experimental data. Overall, multistate PDFT gives quantitative agreement with multistate CASPT2 at a significantly reduced computational cost.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Computation of Auger Electron Spectra in Organic Molecules with Multiconfiguration Pair-Density Functional Theory

Efficient and accurate computation of molecular Auger electron spectra for larger systems is limited by the rapid increase in the number of doubly ionized final states as the system size grows. Here, in this work, we benchmark the application of multiconfiguration pair-density functional theory with a restricted active space (RAS) reference wave function for computing the carbon K-edge decay spectra of 20 organic molecules. Decay rates are computed within the one-center approximation. We evaluate the performance of different basis sets and on-top functionals and find that multiconfiguration pair-density functional theory achieves accuracy comparable to RAS followed by second-order perturbation theory, but at significantly lower computational cost.

Fouda, Adam E. A. [Argonne National Laboratory (AN↗

DOE OSTI2025

The Remarkable I 2 O 3 Molecule: A New View from Theory

Atmospheric iodine chemistry has garnered increasing attention as a result of increased iodine emissions. A key subset of this chemistry involves iodine oxides (I 2 O 2–5 ), which serve as precursors to particle formation. Among these, I 2 O 3 is the simplest iodine oxide involved in particle formation, but it has remained undetected in the atmosphere. Previous theoretical studies have characterized this peculiar molecule, primarily using energies to refine geometries obtained at low levels of theory. Due to the reemerging interest in I 2 O 3 , this study presents geometries optimized at the CCSD(T)/aug-cc-pwCVTZ-PP level of theory─marking the first instance, to the best of our knowledge, where this system has been studied exclusively with CCSD(T). Harmonic vibrational frequencies were computed at the same level of theory. Final energetics were obtained using the very high level CCSDT(Q) method with basis sets up to quintuple-zeta cardinality (aug-cc-pwCV5Z-PP) and extrapolated to the CBS limit to yield CCSDT(Q)/CBS//CCSD(T)/aug-cc-pwCVTZ-PP energies. These energies include harmonic zero-point vibrational energy corrections and scalar relativistic energy corrections. Additionally, this study discovers new isomers along the I 2 O 3 potential energy surface, a novel contribution to the field. The performance of different computational methods and DFT functionals commonly used in atmospheric chemistry is also assessed relative to high-level theoretical methods.

basis sets↗

DOE OSTI2023

Local Molecular Field Theory for Coulomb Interactions in Aqueous Solutions

Coulomb interactions play a crucial role in a wide array of processes in aqueous solutions but present conceptual and computational challenges to both theory and simulations. We review recent developments in an approach addressing these challenges–local molecular field (LMF) theory. LMF theory exploits an exact and physically suggestive separation of intermolecular Coulomb interactions into strong short-range and uniformly slowly varying long-range components. This allows us to accurately determine the averaged effects of the long-range components on the short-range structure using effective single particle fields and analytical corrections, greatly reducing the need for complex lattice summation techniques used in most standard approaches. Furthermore, the simplest use of these ideas in aqueous solutions leads to the short solvent (SS) model, where both solvent–solvent and solute–solvent Coulomb interactions have only short-range components. Here we use the SS model to give a simple description of pairing of nucleobases and biologically relevant ions in water.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Closing the Gap Between Experiment and Theory: Reactive Scattering of HCl from Au(111)

Accurate simulation of molecules reacting on metal surfaces, which can help in improving heterogeneous catalysts, remains out of reach for several reactions. For example, a large disagreement between theory and experiment for HCl reacting on Au(111) still remains, despite many efforts. In this work, the dissociative chemisorption of HCl on Au(111) is investigated with a recently developed MGGA density functional (MS-RPBEl) and a high-dimensional neural network potential. Additionally, previous experimental sticking probabilities are re-examined. A considerably improved agreement between experiment and theory is obtained, although theory still overestimates experimental sticking probabilities by a factor of 2-7 at the highest incidence energy. Computed and measured vibrational transition probabilities are also in improved agreement. Several dynamical effects such as angular steering and energy transfer from the molecule to the surface are found to play an important role.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Wavelength-Dependent Excitonic Properties of Covalent Organic Frameworks Explored by Theory and Experiments

Many aspects of the correlation between physical structure, light harvesting, and excitonic properties of covalent organic frameworks (COFs) remain unclear despite being key properties determining their photocatalytic function. One area of COF research that could bring clarity is through using both electronic structure theory and time-resolved spectroscopic analysis over a series of isomeric COFs. Here, we show structure-property relationships between four imine COFs built from a combination of ditopic and tritopic monomers using transient absorption spectroscopy together with time-dependent density functional theory. We find that monomer selection only moderately affects the charge transfer (CT) behavior of the COFs. Instead, we infer that imine chemistry profoundly impacts CT by acting as a CT mediator. Moreover, we discover two distinct valence bands arising from varying degrees of locally excited/CT mixing, which is responsible for energy dependent exciton dynamics. Finally, we use theory to hypothesize that interlayer interactions can modify excitonic properties that we correlate with tail states commonly observed, but rarely investigated in COFs. Furthermore, these results reveal that imine chemistry should be recognized as a very important factor to consider in the development of COF photocatalysts and the correlation of their structural environment with light harvesting and CT properties that should ultimately determine their photocatalytic function.

14 SOLAR ENERGY↗

DOE OSTI2026

Insights into Nonelectroactive C–C Bond Formation on Cu(100) during Electrochemical CO 2 Reduction from Multiconfigurational Wavefunction Theory

Carbon–carbon (C–C) bond formation is necessary for hydrocarbon (and oxygenate) synthesis beyond methane (and formate/formic acid) during electrochemical CO and CO 2 reduction (ECOR and ECO 2 R). Cu has notable ability to form hydrocarbons compared to other pure metals. In particular, the (100) facet of face-centered cubic Cu forms ethylene competitively with H 2 and methane during both ECOR and ECO 2 R. Past simulations based on density functional theory (DFT) with standard exchange-correlation functional approximations predict fast nonelectroactive C–C bond formation channels involving adsorbed (*) CO together with another *CO, formyl (*CHO), or hydroxymethylidyne (*COH), forming OC*–*CO, OC*–CHO*, and OC*–*COH, respectively. Such simulations support the prevailing hypothesis that emergence of C 2 products is kinetically determined at the early stages of the reduction chemistry. Here we show, via simulations with more accurate many-body, i.e., “correlated”, wavefunction theory (enabled by an embedding scheme), that the coupling of *CO with a *CO or a *COH (previously predicted at the same level of theory to kinetically dominate over *CHO as the one-electron reduction product of *CO) is highly activated (kinetically impeded), with free energy barriers >1 eV, in contradiction to previous DFT-based simulations. Intriguingly, we find that the coupling of two adjacent *COHs incurs only a small barrier (<0.3 eV) and is exoergic (< –1 eV); however, given the predicted low surface mobility of *COH, the emergence of HOC*–*COH is also improbable, at least at low *COH coverages. We therefore conclude that it is highly unlikely for *CO to participate in nonelectroactive C–C bond formation on pristine Cu(100), contrary to conventional wisdom, and that the energetically favorable *COH dimerization may occur only after substantial buildup of *COH on the surface.

adsorption↗

DOE OSTI2024

Unconventional Error Cancellation Explains the Success of Hartree–Fock Density Functional Theory for Barrier Heights

Energy barriers, which control the rates of chemical reactions, are seriously underestimated by computationally efficient semilocal approximations for the exchange-correlation energy. The accuracy of a semilocal density functional approximation is strongly boosted for reaction barrier heights by evaluating that approximation non-self-consistently on Hartree–Fock electron densities, which has been known for ~30 years. Here, the conventional explanation is that the Hartree–Fock theory yields the more accurate density. This work presents a benchmark Kohn–Sham inversion of accurate coupled-cluster densities for the reaction H 2 + F → HHF → H + HF and finds a strong, understandable cancellation between positive (excessively overcorrected) density-driven and large negative functional-driven errors (expected from stretched radical bonds in the transition state) within this Hartree–Fock density functional theory. This confirms earlier conclusions (Kaplan, A. D., et al. J. Chem. Theory Comput. 2023, 19, 532–543) based on 76 barrier heights and three less reliable, but less expensive, fully nonlocal density functional proxies for the exact density.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Exploiting a Shortcoming of Coupled-Cluster Theory: The Extent of Non-Hermiticity as a Diagnostic Indicator of Computational Accuracy

The fundamental non-Hermitian nature of the forms of the coupled-cluster (CC) theory widely used in quantum chemistry has usually been viewed as a negative, but the present paper shows how this can be used to an advantage. Specifically, the non-symmetric nature of the reduced one-particle density matrix (in the molecular orbital basis) is advocated as a diagnostic indicator of computational quality. In the limit of the full coupled-cluster theory [which is equivalent to full configuration interaction (FCI)], the electronic wave function and correlation energy are exact within a given one-particle basis set, and the symmetric character of the exact density matrix is recovered. The extent of the density matrix asymmetry is shown to provide a measure of “how difficult the problem is” (like the well-known T 1 diagnostic), but its variation with the level of theory also gives information about “how well this particular method works”, irrespective of the difficulty of the problem at hand. The proposed diagnostic is described and applied to a select group of small molecules, and an example of its overall utility for the practicing quantum chemist is illustrated through its application to the beryllium dimer (Be 2 ). Future application of this idea to excited states, open-shell systems, and symmetry-breaking problems and an extension of the method to the two-particle density are then proposed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Real-Space Constrained Density Functional Theory Investigation of Site-Specific, Interfacial Charge Recombination Dynamics Across the Au Nanoparticle/TiO 2 Heterojunction

Au nanoparticle (NP)/TiO 2 heterojunction is a representative system to study interfacial charge transfer in photocatalysis and photovoltaics, where suppressing recombination from TiO 2 to Au can enhance hot carrier extraction. We apply real-space constrained density functional theory (CDFT) with Marcus theory to quantify charge recombination time scales across Au/TiO 2 . This approach enables direct control and visualization of charge-separated states, aligning with site-specific probes like time-resolved X-ray photoelectron spectroscopy (trXPS). We find that the charge-separated state features a bipolaron, with recombination dominated by TiO 2 LUMO to Au HOMO transitions, primarily at interfacial Au sites. Marcus rate predictions are benchmarked with surface hopping methods, quantifying differences in time scales and computational efficiency. Lastly, we examine how the Au cluster size affects the free energy change (ΔG) and reorganization energy (λ), explaining trends in closed-shell systems and highlighting challenges for open-shell extrapolations. Overall, CDFT + Marcus theory provides efficient, mechanistically transparent interfacial charge transfer modeling, and we clearly defined its applicability and limitation.

Glenna, Drew M. [Univ. of Idaho, Idaho Falls, ID (↗

DOE OSTI2020

Microscopic Theory of Long-Time Center-of-Mass Self-Diffusion and Anomalous Transport in Ring Polymer Liquids

We construct a microscopic theory at the level of segment-scale correlated space–time intermolecular forces for the long-time center-of-mass (CM) diffusion constant and intermediate-time non-Fickian transport in dense solutions and melts of ring polymers. The approach combines ideas of polymer, colloid, and liquid-state statistical mechanics to quantify how the multifractal intra-ring conformational structure and inter-ring packing correlations determine dynamic caging constraints and time-dependent friction. Breakdown of Rouse theory is predicted to occur due to length scale-dependent temporal correlation of forces exerted on pairs of tagged ring segments from surrounding polymers. At large enough degrees of polymerization (N), a stronger scaling of the CM diffusion constant (D ∝ N –2 ) is predicted, with a crossover N D proportional to the product of the system-specific macromolecular volume fraction and dimensionless compressibility. In analogy with caging effects in glass-forming fluids, the theory does appear to begin to fail at sufficiently high N/N D for the center-of-mass diffusivity, likely due to another crossover to an even slower activated transport regime. However, use of N/N D with the theoretically predicted N D , in conjunction with dynamic blob scaling ideas for local Rouse friction, collapses semidilute and concentrated solution simulation data onto a master curve. Based on the same physical ideas employed to predict the diffusion constant, a generalized Langevin equation description is formulated for intermediate-time CM transport. It predicts two subdiffusive regimes that emerge due to the self-similar nature of internal ring structure. Analytic and numerical predictions for the apparent non-Fickian exponent as a function of time, N/N D and dimensionless compressibility, the evolution of the maximum degree of subdiffusive motion with N/N D , and the time scale for recovering Fickian diffusion are made, all of which are in good accordance with melt simulations. Furthermore, the present work sets the stage to address activated dynamics and glass formation on the macromolecular scale.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Theory of Ion-Mediated Segmental Localization, Activated Structural Relaxation, and the Glass Transition in Polymerized Ionic Liquids

Here we combine polymer integral equation theory for structural correlations with a force-level theory for activated segmental relaxation to construct a microscopic theory for how ions modify the onset of segmental localization, the polymer alpha relaxation time, and glass transition temperature, T g , in dry polymerized ionic liquids (PolyILs). Our most important findings concerning the behavior of T g are (i) a weak dependence on anion–cation Coulomb attraction strength due to strong decoupling of ion and segmental dynamics, (ii) strong reduction with increasing mobile ion size due to both plasticization effects and weakening of ion-modified monomer caging, and (iii) increase with backbone rigidity and intrachain dynamic cooperativity. We quantitatively estimate T g variations as ion size and polymer static and dynamic rigidity are widely varied. The experimental data of 19 PolyILs are organized into a specific pattern consistent with the theoretical predictions with glass transition temperatures varying over a very wide range (~250 K) as observed experimentally. Based on the theoretical results, suggestions are made concerning the search for high conductivity Li- or Na-based PolyILs based on further lowering of T g via new polymer synthesis. Calculations of the alpha time as a function of packing fraction reveal the dynamic fragility increases for larger mobile ions, a more flexible backbone, and/or a smaller degree of intrachain dynamic cooperativity, as a consequence of the increasing importance of collective elasticity in determining the activation barrier. An analysis of transient segmental localization and a crossover to activated dynamics reveals similar, but not identical, trends as predicted at the laboratory vitrification timescale.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Ripening of Rh Nanoparticle Catalysts in Reverse Water–Gas Shift via a Data-Driven Model Combining Physics, Theory, and Experiment

Degradation via sintering is an ongoing challenge that impedes the broad commercial success of supported metallic nanoparticle catalysts. To mitigate degradation via informed catalyst design and process operations, here we aim to disambiguate the underlying mechanisms of sintering by combining theory and experiment in a quantitative framework. While mechanistic sintering models exist, they only model a single sintering pathway, even though multiple sintering mechanisms can occur simultaneously or dominate at different stages of the process. Data-driven machine learning models have emerged as a means to represent complex processes through data regression. However, machine learning models have very large data needs and lack mechanistic insights due to their black-box encoding. To develop an interpretive model of catalyst degradation via sintering, we constructed a hybrid model combining mechanistic “physics-based” models and data-driven methods to obtain both reliable predictions and mechanistic insights regarding experimentally observed sintering phenomena. Focusing on nanoparticle sintering in the Rh–TiO 2 catalyst for the reverse water–gas shift (RWGS) reaction, the hybrid model couples a mechanistic term for Ostwald ripening with energy values calculated via density functional theory (DFT) with a parametric, data-driven discrepancy function term for unmodeled mechanisms. The hybrid model is trained using Bayesian inference with data collected from small-angle X-ray scattering (SAXS) in situ experiments wherein average nanoparticle diameter versus time was measured at three relevant operating temperatures. The calibrated hybrid model results show that an Ostwald ripening-only model parameterized with fixed DFT energies does not fully capture the time and temperature dependence of the SAXS-observed sintering kinetics, and that an additional functional contribution, or DFT energy calibration, is required to reconcile simulation and experiment. Analysis of the hybrid-model error confirms that the hybrid model outperforms both the purely mechanistic and purely data-driven alternatives in terms of expected predictive accuracy for time-evolving average particle sizes. Furthermore, the results support the hypothesis that the Ostwald ripening mechanism is less important for explaining the sintering phenomena as operating temperature increases under an assumed fixed DFT parameterization. This could be explained in one of two ways: either latent, unmodeled sintering mechanisms dominate at higher temperatures, or the DFT uncertainty increases with temperature. The proposed modeling approach directly links theory to experiments and simulations via a statistical hybrid modeling framework and can be extended to other catalytic systems to improve predictive models and mechanistic understanding.

Bayesian hybrid modeling↗

DOE OSTI2021

Integration of theory and experiment in the modelling of heterogeneous electrocatalysis.

Theoretical modelling is essential to deepen our understanding of heterogeneous electrocatalytic energy conversion processes, such as water splitting. Here, Sharon Hammes-Schiffer and Giulia Galli offer their perspectives on the best strategies for successfully studying such systems. Heterogeneous electrocatalysis is critical to many energy conversion processes. Theoretical and computational approaches are essential to interpret experimental data and provide the mechanistic understanding necessary to design more effective catalysts. However, automated general procedures to build predictive theoretical and computational frameworks are not readily available; specific choices must be made in terms of the atomistic structural model and the level of theory, as well as the experimental data used to inform and validate these choices. Here we outline some best practices for modelling heterogeneous systems and present examples in the context of catalysis at metal electrodes and oxides. The level of theory should be chosen for the specific system and properties of interest, and experimental validation is essential from the beginning to the end of the study. Continuous feedback and ultimate integration between experiment and theory enhances the power of calculations to elucidate mechanisms, identify effective descriptors and clarify design principles.

Hammes-Schiffer, Sharon↗

DOE OSTI2023

The unitary dependence theory for characterizing quantum circuits and states

Abstract Most existing quantum algorithms are discovered accidentally or adapted from classical algorithms, and there is the need for a systematic theory to understand and design quantum circuits. Here we develop a unitary dependence theory to characterize the behaviors of quantum circuits and states in terms of how quantum gates manipulate qubits and determine their measurement probabilities. Compared to the conventional entanglement description of quantum circuits and states, the unitary dependence picture offers more practical information on the measurement and manipulation of qubits, easier generalization to many-qubit systems, and better robustness upon partitioning of the system. The unitary dependence theory can be applied to systematically understand existing quantum circuits and design new quantum algorithms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Classical and quantum simulations of 1+1-dimensional ${\mathbb{Z}}_{2}$ gauge theory at finite temperature and density

Simulating strongly coupled gauge theories at finite temperature and density is a longstanding challenge in nuclear and high-energy physics with fundamental implications for condensed matter physics. Here, we simulate such systems using minimally entangled typical thermal state (METTS) approaches, which combine classical random sampling with imaginary-time evolution, implementable on either classical or quantum computers, to estimate thermal averages of observables. We study 1+1-dimensional ${\mathbb{Z}}_{2}$ gauge theory coupled to spinless fermionic matter, which maps onto a local quantum spin chain. We benchmark both a classical matrix-product-state implementation of METTS and a recently proposed adaptive variational approach for near-term quantum devices, focusing on the equation of state and measures of fermion confinement. Of particular importance is the choice of basis for METTS sampling, which impacts both the sampling overhead and quantum circuit complexity. Our work sets the stage for future studies of strongly coupled gauge theories using classical and quantum hardware.

Chen, I-Chi [Iowa State Univ., Ames, IA (United St↗

DOE OSTI2026

Towards AI-assisted neutrino flavor theory design

Particle physics theories, such as those which explain neutrino flavor mixing, arise from a vast landscape of model-building possibilities. A model’s construction typically relies on the intuition of theorists. It also requires considerable effort to identify appropriate symmetry groups, assign field representations, and extract predictions for comparison with experimental data. We develop Autonomous Model Builder (AMBer), a framework in which a reinforcement learning agent interacts with a streamlined physics software pipeline to search these spaces efficiently. AMBer selects symmetry groups, particle content, and group representation assignments to construct models while minimizing the number of free parameters introduced. We validate our approach in well-studied regions of theory space and extend the exploration to a previously unexamined symmetry group. While demonstrated in the context of neutrino flavor theories, this approach of reinforcement learning with physics software feedback may be extended to other theoretical model-building problems in the future.

Baretz, Jason Benjamin↗